Question: "A beam of light has a wavelength of..."

High School
Physics
Light and Optics
Optics

Delaney Escobar

Answered question

2023-01-07

A beam of light has a wavelength of 4.5 x 10^−7 meter in a vacuum. The frequency of this light is ___? (Speed of light is 3*10^8 m/s)

Answer & Explanation

Patricia Gill

Beginner2023-01-08Added 6 answers

6.67 \cdot 10^{14} H z

Explanation: wave equation:

s = f λ

speed = wavelength * frequency
where
s is in metres per second

\frac{m}{s}

f is in hertz Hz
and

λ

is in metres m.

s = f λ

can be rearranged as

f = \frac{s}{λ}

here,

s = 3 \cdot 10^{8} \frac{m}{s}

and

λ = 4.5 \cdot 10^{- 7} m

\frac{s}{λ} = \frac{3 \cdot 10^{8}}{4.5 \cdot 10^{- 7}}

\frac{3}{4.5} = \frac{2}{3} \approx 0.667

\frac{10^{8}}{10^{- 7}} = 10^{8 - - 7} = 10^{8 + 7}

= 10^{15}

0.667 \cdot 10^{15} = 6.67 \cdot 10^{14}

f = 6.67 \cdot 10^{14} H z

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